'meter' (and by extension forms like 'metered') originates from Greek, specifically the word 'metron', where 'metron' meant 'measure'.

'metron' passed into Latin as 'metrum', then into Old French as 'metre', and later into Middle English as 'metre'/'meter' before becoming the modern English 'meter'. The verb sense (to measure or to regulate) developed from the noun (instrument/measure).

Initially it meant 'a measure' or 'instrument for measuring', but over time it evolved to include the verb senses 'to measure' and 'to regulate by measure'; the adjective 'metered' developed to mean 'measured' or 'regulated' and also 'arranged in metrical rhythm'.